Finite Group Databasebeta

← #14780638

Subgroups — #14780638

Order 2816.

2014 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67004C211yesmaximal, characteristic, complemented
2C2×#10623356C211yesmaximal, characteristic, complemented
3C2×#10622846C211yesmaximal, characteristic, complemented
4C22×#66874C211yesmaximal, characteristic, complemented
5C2×#10622847C211yesmaximal, characteristic, complemented
6#13069624C214yesmaximal, complemented
7#13069619C214yesmaximal, complemented
8#13068335C211yesmaximal, characteristic, complemented
9C2×C11×#537C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C22×C11×#41C2211yescharacteristic
12C23×Dic22C2211yescharacteristic
13C11×#537—24no—
14C11×#537—24no—
15C2×C11×C22⋊Q8—21no—
16C2×C11×C22⋊Q8C2212yes—
17C2×C11×#121—21no—
18C2×C11×#121—22no—
19C2×C11×#121C2212yes—
20C22×C11×C4⋊C4C2211yescharacteristic
21#10623356—24no—
22#10623356—24no—
23C2×#67004—24no—
24C2×#67004—24no—
25C2×#67004—24no—
26C2×#66997—21no—
27C22×#4326C2212yes—
28C2×#66989—21no—
29C2×#66988—22no—
30C22×#4324C2212yes—
31C2×#66979C2211yescharacteristic
32C2×#66977C2214yes—
33C22×#4318C2211yescharacteristic
34C23×C11⋊C8C2211yescharacteristic
35#10622847—24no—
36#10622846—24no—
37C2×#66899C2212yes—
38C2×#66896C2212yes—
39C2×C22⋊(C11⋊C8)C2214yes—
40C2×#66874—24no—
41C2×#66874C2214yes—
42#10622167C2214yes—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41—22no—
51C2×C11×#41—22no—
52C2×C11×#41—22no—
53C2×C11×#41—22no—
54C2×C11×#41D414yes—
55C22×Q8×C11D411yescharacteristic
56C22×Q8×C11C2311yescharacteristic
57C22×D4×C11—21no—
58C22×D4×C11—22no—
59C22×D4×C11D412yes—
60C22×D4×C11D411yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11—21no—
64C23×C4×C11C2312yes—
65C23×C4×C11C2311yescharacteristic
66C23×Dic11—21no—
67C22×Dic22—22no—
68C22×Dic22—22no—
69C22×Dic22—22no—
70C22×Dic22—22no—
71C22×Dic22—21no—
72C22×Dic22—22no—
73C22×Dic22D414yescomplemented
74C22×Dic22C2312yes—
75C11×C22⋊Q8—28no—
76C11×C22⋊Q8—24no—
77C11×C22⋊Q8—24no—
78C11×#121—216no—
79C11×#121—28no—
80C11×#121—24no—
81C11×#121—24no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4D414yes—
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C22⋊Dic11—24no—
90C2×C22⋊Dic11—21no—
91#67004—232no—
92#66997—28no—
93C2×#4326—24no—
94C2×#4326—24no—
95C2×#4326—24no—
96#66989—28no—
97#66988—216no—
98C2×#4324—24no—
99C2×#4324—24no—
100C2×#4324—24no—
101#66979—22no—
102#66979D414yescomplemented
103C2×C4⋊Dic11C2312yes—
104#66977—28no—
105#66977—28no—
106C2×Dic11⋊C4—24no—
107C2×C4×Dic11—21no—
108C2×#4318—22no—
109C2×#4318—22no—
110C2×#4318D414yescomplemented
111C22×C11⋊C8—22no—
112C22×C11⋊C8—22no—
113C22×C11⋊C8—22no—
114C22×C11⋊C8C2312yes—
115C22×C11⋊C8C2312yes—
116#66899—24no—
117#66896—24no—
118C22⋊(C11⋊C8)—28no—
119#66874—28no—
120#23394—111nomaximal, Sylow
121C24×C11—21no—
122C24×C11C2×D412yes—
123C24×C11C2×D411yescharacteristic
124C11×#41—28no—
125C11×#41—28no—
126C11×#41—44no—
127C11×#41—44no—
128C11×#41—44no—
129C11×#41—44no—
130C11×#41—44no—
131C11×#41—44no—
132C2×Q8×C11—22no—
133C2×Q8×C11—22no—
134C2×Q8×C11—22no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11C2×D412yes—
141C2×D4×C11—24no—
142C2×D4×C11—24no—
143C2×D4×C11—24no—
144C2×D4×C11—24no—
145C2×D4×C11—28no—
146C2×D4×C11—22no—
147C2×D4×C11—22no—
148C2×D4×C11—22no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—42no—
155C2×D4×C11—42no—
156C2×D4×C11—84no—
157C2×D4×C11C2×D412yes—
158C22×C4×C11—22no—
159C22×C4×C11—21no—
160C22×C4×C11—24no—
161C22×C4×C11—24no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—42no—
169C22×C4×C11—42no—
170C22×C4×C11—82no—
171C22×C4×C11C2×D412yes—
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D412yes—
174C22×C4×C11C2×D412yes—
175C22×C4×C11C2×D412yes—
176C22×C4×C11C2×D412yes—
177C22×C4×C11C2×D412yes—
178C22×C4×C11#4112yes—
179C22×C4×C11C2411yescharacteristic
180C22×Dic11—24no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—42no—
184C22×Dic11—42no—
185C2×Dic22—28no—
186C2×Dic22—24no—
187C2×Dic22—28no—
188C2×Dic22—22no—
189C2×Dic22—22no—
190C2×Dic22—22no—
191C2×Dic22—22no—
192C2×Dic22—22no—
193C2×Dic22—42no—
194C2×Dic22—44no—
195C2×Dic22—42no—
196C2×Dic22—44no—
197C2×Dic22C2×D414yes—
198C11×C4⋊C4—28no—
199C11×C4⋊C4—24no—
200C11×C4⋊C4—22no—
201C11×C4⋊C4C2×D414yes—
202C11×C22⋊C4—28no—
203C11×C22⋊C4—28no—
204C22⋊Dic11—216no—
205C22⋊Dic11—24no—
206#4326—216no—
207#4324—216no—
208C4⋊Dic11—22no—
209C4⋊Dic11C2×D414yes—
210Dic11⋊C4—216no—
211C4×Dic11—24no—
212#4318—28no—
213C2×C11⋊C8—22no—
214C2×C11⋊C8—22no—
215C2×C11⋊C8—22no—
216C2×C11⋊C8—22no—
217C2×C11⋊C8—22no—
218C2×C11⋊C8—44no—
219C2×C11⋊C8C2×D414yes—
220C22×#137—111no—
221C2×#537D1111yescharacteristic
222C2×#536—111no—
223C2×#416—111no—
224C22×#103—111no—
225C2×#408—111no—
226#2001—114no—
227#2000—114no—
228#1736—111no—
229C23×C11—22no—
230C23×C11—22no—
231C23×C11—22no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—22no—
235C23×C11—24no—
236C23×C11—24no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—42no—
240C23×C11—42no—
241C23×C11#12012yes—
242C23×C11#12012yes—
243C23×C11#12112yes—
244C23×C11C22×D411yescharacteristic
245Q8×C11—22no—
246Q8×C11—22no—
247Q8×C11—41no—
248Q8×C11—41no—
249Q8×C11—44no—
250D4×C11—22no—
251D4×C11—22no—
252D4×C11—48no—
253D4×C11—48no—
254D4×C11—41no—
255D4×C11—41no—
256D4×C11—44no—
257D4×C11—88no—
258C2×C4×C11—22no—
259C2×C4×C11—24no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—44no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11—42no—
269C2×C4×C11—42no—
270C2×C4×C11—48no—
271C2×C4×C11—84no—
272C2×C4×C11#12014yes—
273C2×C4×C11#12012yes—
274C2×C4×C11#12012yes—
275C2×C4×C11#12114yes—
276C2×C4×C11#12114yes—
277C2×C4×C11#12112yes—
278C2×C4×C11#12714yes—
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C22×D411yescharacteristic
281C2×C4×C11C22×D411yescharacteristic
282C2×C4×C11C22×D411yescharacteristic
283C2×C4×C11C22×D411yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C2×Dic11—24no—
286C2×Dic11—24no—
287C2×Dic11—42no—
288C2×Dic11—42no—
289C2×Dic11—42no—
290C2×Dic11—42no—
291C2×Dic11—48no—
292Dic22—24no—
293Dic22—24no—
294Dic22—42no—
295Dic22—42no—
296Dic22—48no—
297C11⋊C8—24no—
298C11⋊C8—42no—
299C22×#41C2×D1111yescharacteristic
300C22×#41C2×D1111yescharacteristic
301C23×Q8—111no—
302C2×#137—224no—
303C2×#137—224no—
304C2×#137—224no—
305C22×Q16—112no—
306C22×SD16—112no—
307C22×M16—111no—
308C23×C8—111no—
309#537—24no—
310#537—24no—
311#536—224no—
312#536—224no—
313C2×C4⋊Q8—221no—
314C2×#124—221no—
315C2×#123—222no—
316C2×C22⋊Q8—21no—
317C2×C22⋊Q8—114no—
318C2×C22⋊Q8C2×D1112yes—
319C2×#121—21no—
320C2×#121—22no—
321C2×#121C2×D1112yes—
322C2×#117—111no—
323C22×C4⋊C4C2×D1111yescharacteristic
324#416—224no—
325C2×#103—112no—
326C2×#103—114no—
327C2×#103—224no—
328C2×#102—112no—
329#408—224no—
330C2×C22⋊C8—114no—
331#340—114no—
332C22×C11—22no—
333C22×C11—22no—
334C22×C11—24no—
335C22×C11—24no—
336C22×C11—42no—
337C22×C11—42no—
338C22×C11—42no—
339C22×C11—42no—
340C22×C11—42no—
341C22×C11—42no—
342C22×C11—44no—
343C22×C11—44no—
344C22×C11—82no—
345C22×C11—82no—
346C22×C11#39214yes—
347C22×C11C2×#12011yescharacteristic
348C22×C11C2×#12011yescharacteristic
349C22×C11C2×#12111yescharacteristic
350C22×C11#57712yes—
351C22×C11#57812yes—
352C4×C11—42no—
353C4×C11—42no—
354C4×C11—44no—
355C4×C11#39214yes—
356C4×C11C2×#12011yescharacteristic
357C4×C11C2×#12111yescharacteristic
358C4×C11C2×#12111yescharacteristic
359C4×C11C2×#12711yescharacteristic
360Dic11—44no—
361Dic11—44no—
362C2×#41—22no—
363C2×#41—22no—
364C2×#41—22no—
365C2×#41—22no—
366C2×#41—22no—
367C2×#41—22no—
368C2×#41—22no—
369C2×#41—22no—
370C2×#41—22no—
371C2×#41—22no—
372C2×#41—22no—
373C2×#41C22⋊D1114yes—
374C22×Q8—114no—
375C22×Q8—112no—
376C22×Q8—222no—
377C22×Q8—221no—
378C22×Q8—222no—
379C22×Q8—222no—
380C22×Q8—222no—
381C22×Q8—222no—
382C22×Q8C22⋊D1111yescharacteristic
383C22×Q8C22×D1111yescharacteristic
384C22×D4—21no—
385C22×D4—22no—
386C22×D4C22⋊D1112yes—
387C22×D4C22⋊D1111yescharacteristic
388C22×D4C22×D1111yescharacteristic
389C23×C4—21no—
390C23×C4—21no—
391C23×C4—221no—
392C23×C4C22×D1112yes—
393C23×C4C22×D1111yescharacteristic
394#137—2232no—
395C2×Q16—224no—
396C2×Q16—224no—
397C2×Q16—224no—
398C2×SD16—224no—
399C2×SD16—224no—
400C2×SD16—224no—
401C2×M16—114no—
402C2×M16—222no—
403C2×M16—222no—
404C22×C8—112no—
405C22×C8—112no—
406C22×C8—222no—
407C22×C8—222no—
408C22×C8—222no—
409C4⋊Q8—228no—
410#124—228no—
411#123—2216no—
412C22⋊Q8—28no—
413C22⋊Q8—24no—
414C22⋊Q8—24no—
415C22⋊Q8—228no—
416C22⋊Q8—228no—
417#121—216no—
418#121—28no—
419#121—24no—
420#121—24no—
421#117—114no—
422#117—222no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—112no—
427C2×C4⋊C4—224no—
428C2×C4⋊C4C22⋊D1114yes—
429C2×C4⋊C4C22×D1112yes—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—224no—
434C2×C42—221no—
435#103—224no—
436#103—228no—
437#102—224no—
438C22⋊C8—228no—
439C2×C11—24no—
440C2×C11—82no—
441C2×C11—82no—
442C2×C11C2×#39211yescharacteristic
443C2×C11#300911yescharacteristic
444C2×C11#301111yescharacteristic
445C2×C11#301312yes—
446C2×C11#306312yes—
447C24—21no—
448C24C2×C22⋊D1112yes—
449C24C2×C22⋊D1111yescharacteristic
450#41—28no—
451#41—28no—
452#41—44no—
453#41—44no—
454#41—44no—
455#41—44no—
456#41—44no—
457#41—44no—
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—114no—
467C2×Q8—224no—
468C2×Q8—222no—
469C2×Q8—228no—
470C2×Q8—228no—
471C2×Q8—222no—
472C2×Q8—222no—
473C2×Q8—222no—
474C2×Q8—222no—
475C2×Q8—442no—
476C2×Q8—444no—
477C2×Q8—444no—
478C2×Q8—442no—
479C2×Q8C2×C22⋊D1112yes—
480C2×D4—24no—
481C2×D4—24no—
482C2×D4—24no—
483C2×D4—24no—
484C2×D4—28no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4—84no—
496C2×D4C2×C22⋊D1112yes—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—82no—
510C22×C4—224no—
511C22×C4—222no—
512C22×C4—222no—
513C22×C4—442no—
514C22×C4—442no—
515C22×C4D4×D1112yes—
516C22×C4D4×D1112yes—
517C22×C4D4×D1112yes—
518C22×C4#434112yes—
519C22×C4C2×C22⋊D1112yes—
520C22×C4C2×C22⋊D1111yescharacteristic
521C22×C4C2×C22⋊D1112yes—
522C22×C4C2×C22⋊D1112yes—
523C22×C4C23×D1111yescharacteristic
524Q16—2216no—
525SD16—2216no—
526M16—228no—
527C2×C8—114no—
528C2×C8—222no—
529C2×C8—222no—
530C2×C8—222no—
531C2×C8—222no—
532C2×C8—222no—
533C2×C8—444no—
534C4⋊C4—28no—
535C4⋊C4—24no—
536C4⋊C4—22no—
537C4⋊C4—114no—
538C4⋊C4—2216no—
539C4⋊C4—222no—
540C4⋊C4C2×C22⋊D1114yes—
541C22⋊C4—28no—
542C22⋊C4—28no—
543C22⋊C4—2216no—
544C22⋊C4—224no—
545C42—224no—
546C11#2339411yescharacteristic, complemented, Sylow
547C23—22no—
548C23—22no—
549C23—22no—
550C23—22no—
551C23—24no—
552C23—24no—
553C23—22no—
554C23—22no—
555C23—41no—
556C23—41no—
557C23—42no—
558C23—42no—
559C23#6699012yes—
560C23#6699212yes—
561C23#6700612yes—
562C23C22×C22⋊D1111yescharacteristic
563Q8—22no—
564Q8—22no—
565Q8—41no—
566Q8—41no—
567Q8—44no—
568Q8—224no—
569Q8—224no—
570Q8—442no—
571Q8—442no—
572Q8—448no—
573D4—22no—
574D4—22no—
575D4—48no—
576D4—48no—
577D4—41no—
578D4—41no—
579D4—44no—
580D4—88no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—44no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—48no—
594C2×C4—84no—
595C2×C4—224no—
596C2×C4—224no—
597C2×C4—442no—
598C2×C4—448no—
599C2×C4—442no—
600C2×C4—442no—
601C2×C4—442no—
602C2×C4#6699014yes—
603C2×C4#6699012yes—
604C2×C4#6699114yes—
605C2×C4#6699214yes—
606C2×C4#6699212yes—
607C2×C4#6699314yes—
608C2×C4#6700612yes—
609C2×C4C2×D4×D1111yescharacteristic
610C2×C4C2×D4×D1111yescharacteristic
611C2×C4C2×D4×D1111yescharacteristic
612C2×C4C2×#434111yescharacteristic
613C2×C4C22×C22⋊D1111yescharacteristic
614C2×C4C22×C22⋊D1111yescharacteristic
615C8—224no—
616C8—442no—
617C22—24no—
618C22—22no—
619C22—22no—
620C22—24no—
621C22—44no—
622C22—42no—
623C22—42no—
624C22—42no—
625C22—42no—
626C22—44no—
627C22—42no—
628C22—42no—
629C22—82no—
630C22—82no—
631C22#1062283614yes—
632C22C2×#6699011yescharacteristic
633C22C2×#6699211yescharacteristic
634C22#1062336712yes—
635C22#1062336912yes—
636C22C2×#6700611yescharacteristic
637C4—44no—
638C4—42no—
639C4—42no—
640C4—444no—
641C4—444no—
642C4#1062283614yes—
643C4C2×#6699011yescharacteristic
644C4C2×#6699111yescharacteristic
645C4C2×#6699211yescharacteristic
646C4C2×#6699311yescharacteristic
647C2—24no—
648C2—82no—
649C2—82no—
650C2C2×#1062283611yescharacteristic
651C2#1307789311yescharacteristic
652C2#1307791111yescharacteristic
653C2#1307792812yes—
654C2#1307830912yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#537C2
socleC23×C11C22×D4
hypercenterC2×#537D11
hypocenterC11#23394
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#67004C2semidirect
2. C2×#10623356C2semidirect
3. C2×#10622846C2semidirect
4. C22×#66874C2semidirect
5. C2×#10622847C2semidirect
6. #13069624C2semidirect
7. #13069619C2semidirect
8. #13068335C2semidirect
73. C22×Dic22D4semidirect
102. #66979D4semidirect
110. C2×#4318D4semidirect
546. C11#23394semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#670042
C2×#106233562
C2×#106228462
C22×#668742
C2×#106228472
#130696242
#130696192
#130683352
C2×C11×#5372
#2339411